244 Mr. Crichton on Expansions. [April, 



giving, besides, for elongation of a glass rod taken as 1 at freez- 

 ing, — : at boiling water, instead of t-^j. 



If the above reasoning be conclusive, it necessarily follows, 

 that the corrections for the expansion of glass, as applied to the 

 air and mercurial thermometers, in their after detailed experi- 

 ments on capacity for caloric, and the relative times of cooling, 

 must, to this extent, have been defective. 



The fallacies which MM. Dulong and Petit have inadvert- 

 ently overlooked, affect not only all calculations where expan- 

 sion of glass should be attended to, but must have led to false 

 results as to the dilatations of the metals in table 4, p. 141, §ven 

 though the premises in the preceding page were true, viz. that 

 H le volume sorti represente evidemment la somme des dilata- 

 tions du mercure et du metal diminuee de la dilatation du verre." 

 Now this formula is manifestly wrong, since the volume driven 

 out does not represent the dilatation of the mercury, and that of 

 the vessel we have shown to be overrated. 



By the above corrected method, the absolute dilatation of 

 water, from its state of maximum density at 42-3° to 212°, was 



found to be ^rr. This number is greater than that generally 



received ; but as 39° has sometimes been assumed as the point 

 of greatest density, instead of 42-3°, this circumstance, which 

 is in effect the same as if 45*6° had been adopted, will, to a cer- 

 tain extent, account for the variation. 



The same method gave for the dilatation of air by the increase 



of temperature from 32° to 212°, ^^ & , M. Lussac found -^^ 



though by means which few will think capable of minute preci- 

 sion. The vessel used in my trial was hermetically sealed at 

 the extremes of temperature ; this sealing was performed at an 

 opening through a capillary fibre, and to ensure complete dry- 

 ness, the vessel had been long heated fully to redness just before 

 making the experiment. 



In the Memoir, MM. Dulong and Petit particularly mention, 

 that they found all the varieties of glass which they used, to have 

 the same expansive power ; this appears surprising, for 1 can 

 truly afhrm, that every specimen of crystal differs more or less 



from another ; trials by mercury give from — - to ^r^, as the 



fractions expelled, in the range from freezing, to boiling water, 



even while the mercury has undergone the same rigorous and 



repeated boilings, these fractions indicating elongations of glass 



ii 

 rods, by that increase of temperature, from -^^ to y^. 



That crystal which is the most colourless is commonly the 

 most ductile and least expansible ; but neither from its specific 

 gravity, nor from its tint, as seen through the axis of a tube, can 



